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Abstrak :
Metode jackknife empirical likelihood adalah suatu metode statistika untuk membentuk interval kepercayaan bagi suatu parameter. Metode jackknife empirical likelihood merupakan pengembangan dari metode empirical likelihood ketika parameternya berbentuk fungsi nonlinier. Metode empirical likelihood sendiri merupakan metode statistika yang digunakan untuk membentuk interval kepercayaan untuk suatu parameter berdasarkan data yang diperoleh dari suatu pengamatan. Pada tugas akhir ini, akan dibahas mengenai pembentukan interval kepercayaan untuk mean absolute deviation dari suatu populasi menggunakan metode jackknife empirical likelihood. Mean absolute deviation itu sendiri merupakan salah satu dari ukuran penyebaran data, yaitu rata-rata harga mutlak dari simpangan data terhadap meannya. Distribusi asimtotik dari fungsi jackknife empirical likelihood ratio adalah suatu distribusi chi-kuadrat dengan derajat bebas satu. Fungsi jackknife empirical likelihood ratio ini akan digunakan untuk membentuk interval kepercayaan untuk mean absolute deviation.

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Jackknife empirical likelihood method is a statistical method to construct the confidence interval for a parameter. Jackknife empirical likelihood method is modification of empirical likelihood method when the parameter is nonlinear function. Empirical likelihood method itself is one of the statistical method used to construct the confidence interval for a parameter based on the data obtained from an experiment. In this paper, we will discuss the construction of the confidence interval for the mean absolute deviation of a population using jackknife empirical likelihood method. Mean absolute deviation itself is one of the measures of dispersion of data, which is the average of the absolute deviations of the data set from its mean. The asymptotic distribution of jackknife empirical likelihood ratio function is a chi square distribution with one degree of freedom. Jackknife empirical likelihood ratio function will be used to construct confidence interval for the mean absolute deviation.

Abstrak :
This paper aims to estimate the stress-strength reliability parameter R = P(Y < X) using progressive type-ll censored data, when X and Y are two independent inverse Weibull variates with different scale parameters but having common shape parameter. The maximum likelihood estimator (MLE) and approximate maximum likelihood estimator (AMLE) of R are derived. Bayes estimation procedure for R has been also discussed with independent gamma priors and squared error loss function (SELF). Further, a comparative study among MLEs, AMLEs, and Bayes estimates is conducted using simulation approach. Finally, a real-life application of the proposed methodology through considered model is provided using head-neck cancer data.

Abstrak :
Recently, a varied L ranked set sampling (VLRSS) scheme has been introduced in the literature for estimating the population mean. The VLRSS scheme is a cost-efficient alternative to the classical ranked-set sampling (RSS) and median RSS (MRSS) schemes. In this paper, we construct a new cumulative sum (CUSUM) control chart for efficiently monitoring the process mean using VLRSS, named the CUSUM-VLRSS chart. The CUSUM-VLRSS chart encompasses the existing CUSUM charts based on RSS and MRSS schemes, named the CUSUM-RSS and CUSUM-MRSS charts. We use extensive Monte Carlo simulations to compute the run length characteristics of the proposed CUSUM chart. It is shown that the CUSUM-VLRSS chart is able to perform uniformly better than the CUSUM-RSS and CUSUM-MRSS charts when detecting different kinds of shift in the process mean. A similar trend is observed when the proposed CUSUM chart is constructed under imperfect rankings. A real data-set is also used to explain the implementation of the CUSUM-VLRSS chart.